Reducing probability of glass breakage in drug delivery devices

ABSTRACT

A method for determining predicted failure rates of drug injection devices includes receiving a set of parameters that specify physical properties of (i) a syringe, and (ii) a liquid drug, and (iii) a drug injection device configured to deliver the liquid drug to a patient via the syringe. The method further includes receiving failure rate data that specifies a measured rate of failure of the drug injection device in response to various peak pressures within the syringe, applying the received set of parameters to a kinematic model of the drug injection device to determine a predicted peak pressure within the syringe, including determining the predicted peak pressure as a function of impact velocity of the liquid drug, determining a probability of failure of the drug injection device using (i) the received failure rate data and (ii) the predicted peak pressure, and providing an indication of the determined probability of failure to an output device.

CROSS-REFERENCE TO RELATED APPLICATIONS

Priority is claimed to U.S. Provisional Application No. 62/308,578,filed Mar. 15, 2016, the entire contents of which are expresslyincorporated herein by reference.

FIELD OF THE DISCLOSURE

The present disclosure relates to injection devices for drug delivery.More particularly, the present disclosure relates to determining theprobability of failure of an autoinjector having a certainconfiguration, and modifying one or several parameters of theautoinjector to improve its reliability.

BACKGROUND

Drug delivery devices, such as autoinjectors, on-body injectors andhand-held injectors, are commonly prescribed for patients toself-administer medication. Such devices typically include a mechanism(e.g., a spring) that operates on a pre-filled syringe in response to atriggering event, such as the patient pressing a button on the device.The mechanism drives the needle into the patient and operates on theplunger to deliver the medication subcutaneously via the needle. Thesedrug delivery devices may be constructed as single-use or reusabledevices.

Autoinjectors and on-body injectors offer several benefits in deliveryof medication as compared to conventional syringes, such as simplicityof use. However, a mechanism may exert excessive force on a glasssyringe, causing breakage. Due to the interaction of multiple parts in adrug delivery device, breakage in general is difficult to predict.

SUMMARY

Disclosed herein are techniques for determining the probable failurerate of a drug delivery device having certain parameters, and using theprobable failure rate in designing the drug delivery device. The drugdelivery device can be an autoinjector with a mechanism that drives aneedle and a plunger of a syringe in order to subcutaneously deliver adrug. As discussed below, a system of this disclosure can apply one orseveral parameters of an autoinjector (e.g., spring constant), a glasssyringe (e.g., mass), and drug product (e.g., fluid density) to a 1Dkinematic model of the drug delivery device to generate a prediction ofthe peak pressure within the glass syringe. The system then candetermine, based on the predicted peak pressure and empirical data thatrelates peak pressure to probability of failure, the probability thatthe autoinjector under consideration will fail.

One example embodiment of these techniques is a non-transitorycomputer-readable medium storing instructions. When executed on one ormore processors, the instructions implement a method for determiningpredicted failure rates of drug injection (or “drug delivery”) devices.The method includes receiving a set of parameters that specify physicalproperties of (i) a syringe, and (ii) a liquid drug, and (iii) a druginjection device configured to deliver the liquid drug to a patient viathe syringe. The method also includes receiving failure rate data thatspecifies a measured rate of failure of the drug injection device inresponse to various peak pressures within the syringe, applying thereceived set of parameters to a kinematic model of the drug injectiondevice to determine a predicted peak pressure within the syringe,including determining the predicted peak pressure as a function ofimpact velocity of the liquid drug, and determining a probability offailure of the drug injection device using (i) the received failure ratedata and (ii) the predicted peak pressure. The method further includesproviding an indication of the determined probability of failure to anoutput device.

Another example embodiment is a method for manufacturing drug injectiondevices. The method includes receiving, by one or more processors, afixed set of parameters that specify physical properties of a syringeand a liquid drug. The method further includes determining a set ofparameters that specify physical properties of a drug injection deviceconfigured to deliver the liquid drug to a patient via the syringe,including: (i) generating, by the one or more processors, a candidateset of parameters for the drug injection device, (ii) applying, by theone or more processors, the fixed set of parameters and the candidateset of parameters to a kinematic model of the drug injection device todetermine a predicted peak pressure within the syringe, includingdetermining the predicted peak pressure as a function of impact velocityof the liquid drug, (iii) determining, by the one or more processors, aprobability of failure of the drug injection device using the determinedpredicted peak pressure, (iv) if the probability of failure is above athreshold value, repeating the steps (i)-(iii) with a modified candidateset of parameters, and (v) selecting the candidate set of parameters ifthe probability of failure is not above the threshold value. The methodfurther includes manufacturing the drug injection device using thedetermined set of parameters.

Still another embodiment of these techniques is a drug injection deviceconfigured to deliver a liquid drug to a patient via a syringe. The druginjection device is prepared by a process including receiving a fixedset of parameters that specify physical properties of a syringe and aliquid drug, determining a set of parameters that specify physicalproperties of a drug injection device configured to deliver the liquiddrug to a patient via the syringe, and using the determined set ofparameters to manufacture the drug injection device. Determining the setof parameters includes (i) generating a candidate set of parameters forthe drug injection device, (ii) applying the fixed set of parameters andthe candidate set of parameters to a kinematic model of the druginjection device to determine a predicted peak pressure within thesyringe, including determining the predicted peak pressure as a functionof impact velocity of the liquid drug, (iii) determining a probabilityof failure of the drug injection device using the determined predictedpeak pressure, (iv) if the probability of failure is above a thresholdvalue, repeating the steps (i)-(iii) with a modified candidate set ofparameters, and (v) selecting the candidate set of parameters if theprobability of failure is not above the threshold value.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an example computing system in which thetechniques of the present disclosure can be implemented.

FIG. 2A illustrates a cross-section of a proximal portion of anautoinjector which the system of FIG. 1 can model, in an enlargedperspective view.

FIG. 2B illustrates a cross-section of a distal portion of theautoinjector of FIG. 2A, in an enlarged perspective view.

FIG. 3A illustrates an example autoinjector which the system of FIG. 1can model, prior to initiating of a firing sequence.

FIG. 3B illustrates the autoinjector of FIG. 3A at the first stage ofthe firing sequence, where a needle shield is removed.

FIG. 3C illustrates the autoinjector of FIG. 3A at the second stage ofthe firing sequence, where a patient presses the button to cause aspring to advance a plunger rod and a syringe driver.

FIG. 3D illustrates the autoinjector of FIG. 3A at the third stage ofthe firing sequence, where the syringe driver advances the needle intothe patient.

FIG. 3E illustrates the autoinjector of FIG. 3A at the fourth stage ofthe firing sequence, where the plunger rod disengages the syringe driverand advances to the plunger.

FIG. 3F illustrates the autoinjector of FIG. 3A at the fifth, last stageof the firing sequence, where the plunger extrudes the drug from thesyringe.

FIG. 4A is a pre-impact kinetic diagram, according to which the systemof FIG. 1 can model an autoinjector.

FIG. 4B is a simplified pre-impact kinetic diagram, according to whichthe system of FIG. 1 can model an autoinjector.

FIG. 5A is a first-impact kinetic diagram, according to which the systemof FIG. 1 can model an autoinjector.

FIG. 5B is a simplified first-impact kinetic diagram, according to whichthe system of FIG. 1 can model an autoinjector.

FIG. 5C is an extended first-impact kinetic diagram with boundaryconditions, according to which the system of FIG. 1 can model anautoinjector.

FIG. 6A is a second-impact diagram, according to which the system ofFIG. 1 can model an autoinjector.

FIG. 6B is a simplified second-impact diagram, according to which thesystem of FIG. 1 can model an autoinjector.

FIG. 7 is a graph that illustrates fitting syringe driver friction toexperimental data, which the system of FIG. 1 can use with a model of anautoinjector.

FIG. 8 is a graph that illustrates fitting plunger damping toexperimental data, which the system of FIG. 1 can use with a model of anautoinjector.

FIG. 9 is a graph that illustrates fitting plunger-syringe friction toexperimental data, which the system of FIG. 1 can use with a model of anautoinjector.

FIG. 10 is a graph that illustrates experimental data indicative of peakmeasured force on a syringe carrier as a function of impact velocity,which the system of FIG. 1 can use with a model of an autoinjector.

FIG. 11 illustrates predicted distributions of peak pressures, which thesystem of FIG. 1 can generate using a model.

FIG. 12 is a flow diagram of an example method for determining predictedfailure rates of drug injection devices, which can be implemented in thesystem of FIG. 1.

FIG. 13 is a flow diagram of an example method for manufacturing a druginjection device using the system of FIG. 1.

Same reference numerals are used in the drawings to identify same orsimilar elements and structures in the various embodiments.

DETAILED DESCRIPTION System Overview

FIG. 1 is a block diagram of an example computing system 10 in whichsome of the modeling and parameter selection techniques of thisdisclosure can be implemented.

The computing system 10 can include a single computer, a portablecomputer, a server or a group of servers. In an example implementation,the computing system 10 includes one or more processors 12 (e.g., CPUs),a user interface 14 (e.g., a touchscreen, a monitor and a keyboard), anetwork interface 16 configured for wired and/or wirelesscommunications, a non-transitory computer-readable program memory 18, aparameter data storage 20, and a historical data storage 22,interconnected by a communication link such as a digital bus. Theprogram memory 18 can include persistent (e.g., a hard disk) as well asnon-persistent (e.g., RAM) components. The storage components 20 and 22can be implemented in a local or remote memory in accordance with anysuitable data storage techniques (e.g., as a relational database).

A modeling system 30 can be stored in the program memory 18 as a set ofinstructions executable on the one or more processors 12. The modelingsystem 30 can include an injector modeling module 32 that receivesindications of properties of a drug delivery device, a syringe on whichthe drug delivery device operates, and a drug delivered by the drugdelivery device to a patient via the syringe. Using these parameters,the injector modeling module 32 generates a peak pressure predictionwithin the syringe based on the input in accordance with a kinematicmodel 40.

An example implementation of the kinematic model 40 is discussed belowwith reference to FIGS. 4A-6B. Examples of properties the injectormodeling module 32 can receive as input are discussed below withreference to various drawings. Potential and/or actual values of theseproperties can be retrieved from the parameter data storage 20, which inturn can receive these values via the user interface 14 or the networkinterface 16, from a parameter selection module 50 that can generatecandidate values automatically. In various scenarios, the parametersdefining input to the injector modeling module 32 can correspond toparameters of existing devices or components or candidate parameters fordevices or components being designed.

The modeling system 30 also can include a probability of failurecalculation module 60 that receives the peak pressure prediction fromthe injector modeling module 32 as well as empirical failure data forpeak pressure values, which can be stored in the historical data storage22, for example. The probability of failure calculation module 60determines a probability of failure using a statistical technique suchas the two-term Weibull distribution.

The probability of failure calculation module 60 can provide anindication of the determined probability to a user via the userinterface 14. Moreover, in some implementations, the parameter selectionmodule 50 can use the probability of failure output by the module 34 toselect a new set of candidate parameters. As discussed in more detailbelow with reference to FIG. 8, the parameter selection module 50 caniterate through various candidate values to identify parameters thatyield a sufficiently low probability of failure. The parameters then canbe used in manufacturing.

If desired, the injector modeling module 32 can be implemented in oneserver or group of servers, and the parameter selection module 50 can beimplemented in another server or group of servers. More generally, thecomponents illustrated in FIG. 1 can be distributed among multiplesystems and interconnected in any suitable manner.

Next, an example autoinjector the system of FIG. 1 can model isdiscussed with reference to FIGS. 2A and 2B. An example succession ofoperational states of this autoinjector (the “firing sequence”) is thendiscussed with reference to FIGS. 3A-F. It is noted, however, that atleast some of the techniques of this disclosure similarly can be appliedto other drug delivery devices. For example, drug delivery devicesgenerally suitable for simulation using the techniques of thisdisclosure can include hand-held injectors.

More generally, the techniques of this disclosure can be applied todevices in which a component that advances a liquid drug (or anotherliquid) uses coil compression, torsion, or another type of mechanicalenergy storage. Moreover, these techniques can be applied tonon-mechanical systems such as propellant-driven systems.

Example Autoinjector and Firing Sequence

An example autoinjector 100 includes a proximal end 102 illustrated inFIG. 2A and a distal end 104 illustrated in FIG. 2B. The autoinjector100 is of a type for which the modeling system 30 can generate apredicted peak pressure and determine the probability of failure.However, the autoinjector 100 is only one example of a suitable drugdelivery device, and the modeling system 30 in general can model glassbreakage in a wide variety of devices in which a mechanism exerts aforce on a syringe to deliver a drug to a patient. As a more specificexample, the modeling system 30 can model glass breakage in a drugdelivery device that, unlike the autoinjector 100, does not include theauto-insertion.

The autoinjector 100 can be configured as a pen-type device. Someembodiments of the autoinjector 100 can be configured as a disposable,single use device which delivers a fixed dose of the drug. In otherembodiments, the autoinjector 100 may be configured as a reusabledevice. Reusable drug injection devices 10 may be constructed to delivera multiple doses of a drug where the doses of the drug may be fixed oruser/patient-settable.

Referring first to FIG. 2A, the autoinjector 100 comprises a shell orhousing 106, which may be open at the distal end 104 and closed at theproximal end 102. The housing 106 can be constructed as a single,unitary component or constructed from multiple components or sectionsthat are combined into a single, integral unit. The housing can be madeof plastic, for example.

The housing 106 encloses an actuator 102 and an actuator sleeve 104. Aspring 106 is disposed along a spring guide rod 108 inside a plunger rod110. As illustrated best in FIG. 2B, a plunger-stopper (or simply“plunger”) 112 is positioned on a same virtual axis as the plunger rod110. Collectively, the components 102-110 can be referred to as the“power pack,” as these components store, and release during operation,kinetic energy used by the autoinjector 100. As further illustrated inFIG. 2B, a glass syringe 120 is encased within a syringe carrier 122.The plunger 112 is moveable through the chamber of the syringe 120 toadvance a fluid column (i.e., the drug) toward a shoulder 128 and into aneedle 124. The portion of the syringe 120 that contains a portion ofthe needle 124 defines a cone area 130, and the opposite side of thesyringe 120 defines a flange 121. A needle shield 126 removeablyencloses the cone area 130 and the needle 124 prior to activation of theautoinjector 100. Prior to removal, the needle shield 126 is within afront shell 132, which is a portion of the housing 106.

In operation, the patient removes the needle shield 120, places theautoinjector 100 against her skin, and depresses the activation button(not shown) or otherwise initiates operation of the autoinjector 100.The actuator 102 releases the energy of the compressed spring 106. Inresponse, the spring 106 drives the plunger rod 110, which in turnadvances the plunger 112 and the syringe driver 114.

Analysis of the autoinjector 100 using high-speed video have revealedthat two events impart significant impact forces to the syringe. Thefirst event is occurs when the moving plunger rod 100 comes in contactwith the stationary plunger 112 upon initial activation of theautoinjector 100. The second impact event occurs when the moving syringecarrier 122 contacts the stationary front shell 132 and the end ofneedle extension. The forces of these two impacts can break glass at lowoccurrence rates. If the plunger 112 is placed lower in the syringe 120,the first impact becomes more important, i.e., more likely to be thecause of breakage. Here, plunger depth refers to distance between thetop of the flange 121 to the top of the plunger 120. Accordingly,“higher” refers to the plunger 120 being closer to the flange 121, and“lower” refers to the plunger 120 being farther away from the flange 121and closer to the needle 124.

More particularly, when the plunger rod 110 strikes the plunger 112, animpact is generated. The load generates pressure waves that propagatethrough the fluid column. For the combination of materials andgeometries typical of glass syringes, a pressure wave will “couple” tothe glass barrel as it propagates axially. This coupling results in areduction of wave speed, and radial motion of the syringe 120. Thecoupled wave oscillates through the syringe 120.

After the plunger rod 110 impacts the plunger 112, the plunger rod 110,the syringe 120, and the syringe carrier 122 advance together. Thismotion inserts the needle 124 into the patient. A second impact load isgenerated when the syringe carrier 122 impacts the internal stop on theshell 132. The second impact produces a second pressure wave thatradiates through the same components. Both the plunger rod 110 strikeagainst the plunger 112 and the syringe carrier 122 strike against thefront shell 132 produce similar pressure waves. The pressure waveresults in a local stress that in low occurrences may result infracturing of the glass syringe 120.

FIGS. 3A-E illustrate an example firing sequence of an autoinjector. Forconvenience, the sequence is discussed with reference to theautoinjector 100 of FIGS. 2A and 2B. The firing sequence can takeseveral milliseconds to complete.

FIG. 3A illustrates the autoinjector 100 prior to the initiation of thefiring sequence. The autoinjector 100 is loaded with the glass syringe100, pre-filled with a liquid drug. At this stage, the needle shield 126covers the needle 124. The spring 106 has not been actuated.

At the stage depicted in FIG. 3B, the patient removes the needle shield126, exposing the needle 124. The patient then patient presses a buttonto activate the device (FIG. 3C). As a result, the spring 106 acts uponthe plunger rod 110 and the syringe driver 114. In response, the plungerrod 110 along with the syringe driver 114 starts to advance in thedirection of the needle 124. In this example implementation, the syringedriver 114 advances with the plunger rod 112 due to interference fit.

Next, at the stage of FIG. 3D, the plunger rod 110 along with thesyringe driver 114, the syringe 120, and the syringe carrier 122 startsto advance in the direction of the point on the patient's body where thedrug is to be administered. The plunger rod 110 and the syringe driver114 advance sufficiently far to drive the needle 124 into the skin.After this step, the syringe driver 114 no longer advances at the samerate as the plunger rod 110.

Now referring to FIG. 3E, the plunger rod 110 at this point disengagesthe syringe driver 114 and advances to impact the plunger 112, whichbegins to extrude the drug out of the syringe 120. The plunger 112 thenextrudes the drug from the syringe 120 via the needle 11, as illustratedin FIG. 3F.

In the sequence of FIGS. 3A-F, the plunger rod 110 does not make contactwith the plunger 112 before the syringe driver 114 causes the syringe120 to advance. In another sequence according to which the autoinjector100 can operate, the plunger rod 110 releases form the syringe driver114 early in the sequence. The plunger rod 110 then impacts the plunger112 before the syringe 120 and the needle 124 are driven into thepatient. As indicated above, the impact of the plunger rod 110 on theplunger 112 is referred to in the discussion of modeling as the “firstimpact,” and the event corresponding to the syringe carrier 114 comingto a stop at the end of the travel is referred to as the “secondimpact.”

In an example implementation of an autoinjector 100, it has beenobserved that the plunger rod 110 moves forward slowly over a smalldistance (e.g., approximately 2 mm) upon activation. Subsequently, theautoinjector 100 fully releases the plunger rod 110, and the modelenters a pre-impact period. At this time, the syringe carrier 122 alsomoves forward (e.g., travelling approximately 0.4-1.2 mm).

1D Kinematic Model

Referring back to FIG. 1, the model 40 can be used to model behavior ofdrug delivery devices such as the autoinjector 100 discussed above.Generally speaking, the model 40 is based on conservation of momentum,with the spring 106 discussed above being the driving force. The model40 uses a set of 1D force-balance equations to predict pressure historywithin the barrel of the syringe 120 and determine dynamic responses ofthe components of the autoinjector 100 as a function of time. Moreparticularly, the model 40 describes the kinematics of the autoinjector100 and can be used to calculate the timing and magnitude of thepressure waves generated within the syringe. To this end, the model 40uses the Korteweg equation to predict peak pressure as a function ofimpact velocities. As discussed in more detail below, the model 40models acoustics using method of characteristics (a technique forsolving partial differential equations), with the addition of a uniqueboundary condition. The model 40 thus can capture the fluid-structureinteraction between the glass of the syringe and drug product, whichotherwise is difficult to model.

Some of the activation parameters of the model 40 can be developedhigh-speed cameras to capture velocities of the moving components of anautoinjector similar to the autoinjector 100. The masses of theindividual components of the autoinjector 100 can be measured usingconventional techniques. The spring constant(s) can be measuredstatically. The geometric dimensions of the components of theautoinjector 100 can be obtained using schematics or lab measurements.Further, the model 40 can be validated using experimental data mapped toinputs and outputs to the model 40.

The spring 106 is modeled as a linear spring with an equilibrium length.For the purposes of the model 40, only the overall dynamics of theplunger 112 are important, and the plunger 112 is represented by aspring and a parallel dashpot. The fluid column (i.e., the drug product)in the device is modeled as an acoustic media, which interacts with theglass syringe through fluid-structure interactions. High-speed videoanalysis has shown that very small amounts of drug product were extrudedduring activation of the autoinjector. To model this pressure release,the needle end of the fluid column was modeled with a combination ofacoustic theory and Hagen-Poiseuille theory. Much like the plunger, theinteraction of the syringe with the carrier/front shell is modeled as aparallel spring and dashpot.

The output of the 1D kinematic model is peak pressure at the end of theneedle (where, according to empirical data, breakage occurs). These peakpressures can be separated into the peak pressures associated with firstand second impact.

The model 40 is based on several assumptions. These assumptions arebased on experimental testing, and/or high-speed video analysis, and/orknown theoretical approaches.

As an initial matter, the model 40 is based on the observation that 2Dand 3D effects are not significant (based on experiments with 2D and 3Dmodels, which exhibit similar behavior to 1D model within the syringe).Further, the model 40 can operate according to the assumption that glassbreakage is independent of method of pressure generation. Still further,the model 40 can rely on peak dynamic pressure to predict glassbreakage.

Simplifications related to fluid properties and flow can include thefollowing: Hagen-Poiseuille flow develops instantaneously in needle;drug product is modeled as Newtonian fluid; pressure wave phenomena areapproximated through method characteristics 1D shock tube solution;speed of sound in the drug product is equivalent to water; flow throughthe barrel acts as a 1D plug flow; and peak pressure in the barreldrives stress in the funnel. Simplifications related to the spring caninclude the following: the spring and the overall actuation componentact as an ideal linear spring with one source of damping; dampingoriginates from the syringe driver which is approximated through a dryfriction model; spring acts as a free spring contributing ⅓ of its massdynamically; and spring dynamic and static force behavior areequivalent. Simplifications related to elasticity and viscosity caninclude the following: plunger-stopper acts as Voigt visco-elasticmodel; plunger elasticity behaves non-linearly; plunger dynamic andstatic elasticity is equivalent; plunger viscosity behaves linearly;conservation of momentum applies instantaneously to the top portion ofthe plunger upon impact; and the syringe and the syringe carrier do notmove independently of one another. Other simplifications can include thefollowing: air gap, when present, compresses adiabatically; cavitationand air bubbles provide negligible damping effect; cavitation is notsignificant for glass breakage; and patient skin is modeled as rigidbody.

Experiments have shown that an air gap can be present between the fluidcolumn (i.e., the drug) and the plunger 112, when the autoinjector 100is held vertically. In a horizontal orientation, which sometimes is usedto deliver the drug, the air forms a bubble that can move within thesyringe 120. This air gap can reduce the peak pressure substantiallyonly when it is large (e.g., several mm in diameter); otherwise, the airgap can reduce peak pressure only marginally. Because the orientation ofthe autoinjector 100 cannot be assumed, and because of the othersimplifications and/or assumptions listed above, the air gap is not usedin the model 40. In other embodiments of the injector modeling module32, however, the air gap can be explicitly accounted for.

Next, the model 40 is discussed in detail with reference to the diagramsof FIGS. 4A-6B.

To more clearly distinguish between idealized elements and theircounterparts in an example implementation of the autoinjector 100, thecomponents of a modeled autoinjector are illustrated using differentreference numbers. Thus, FIG. 4A illustrates a pre-impact kineticdiagram of a system 200 that includes a spring 202 rigidly fixed at oneend and coupled to a plunger rod 204 at the other end. The plunger rod204 is in an interference fit with a syringe driver 206. The plunger rod204 is moveable toward a plunger 208 as the spring 202 decompresses.

Input parameters for the model 40, and the corresponding notation, aresummarized below in the next subsection. In addition to these inputs,the discussion below uses the following notation: x_(object) refers tothe position of an object, x_(object) ^(o) refers to the initialposition of an object, u_(object) refers to velocity of an object,u_(object) ^(o) refers to the initial velocity of an object, P_(atm)refers to the atmospheric pressure, H=x_(meniscus) ^(o) 0−x_(plunger)^(o) 0 refers the initial height of the air gap, A_(barrel)=πD_(barrel)²/4 refers to the cross-sectional area of syringe interior, x refers toposition in syringe, P(x, t) refers to pressure in syringe, u(x, t)refers to velocity in syringe, a refers to Kortaweg wave speed, andR=D_(barrel) ²/2 refers to the inner radius of syringe.

After activation, the model 400 separates the system 200 into twocomponents. The first component is the plunger rod 204 and the spring202, which includes the effective mass for the spring 202. In anidealized spring-mass system (spring of constant mass per unit length),the linear velocity of the spring 202 is accounted for by lumping ⅓ ofthe total spring mass into the mass:

$\begin{matrix}{M_{{rod} + {spring}} = {M_{rod} + \frac{M_{spring}}{3}}} & (1)\end{matrix}$

The second component includes the remaining components besides the shellof the device (autoinjector):

M _(carrier) _(_) _(assembly) =M _(plunger) +M _(syringe) +M _(fluid) +M_(carrier)  (2)

As illustrated in FIG. 4B, two forces act on the plunger rod 204 andsyringe components. A spring force pushes on the plunger rod-springcomponent, and a frictional force (transmitted through the syringedriver) connects the plunger rod 204 with the rest of the autoinjector.The dynamic friction force is assumed to be a constant. In an exampleembodiment, the dynamic friction force is experimentally determined tohave the values between 3 and 10N. The spring law is linear withequilibrium lengths of 13-18 cm and spring constants of 150-500 N/m, inan example embodiment. The equilibrium length and the spring constant ofcourse depend on the spring type and individual variations. First, thespring plastically deforms a significant amount when placed into thecomponent of the autoinjector responsible for driving the syringe (seeFIG. 2A), and second, measuring the spring force within the autoinjectorautomatically accounts for extra internal friction not present in abare-spring system.

Applying Newton's law, F=ma, to the two component leads to equations ofmotions (3) and (5) illustrated below. The initial conditions,illustrated in equations 6-9, state that both masses begin to rest withknown positions. In the equations below, over dots denote derivativeswith respect to time.

M _(rod+spring) {umlaut over (x)} _(rod+spring) =F _(spring) −F_(friction)  (3)

F _(spring) =−k({umlaut over (x)} _(rod+spring) −L)  (4)

M _(carrier) _(_) _(assembly) {umlaut over (x)} _(carrier) _(_)_(assembly) =F _(friction)  (5)

x _(rod+spring)(t=0)=x _(rod+spring) ⁰  (6)

x _(carrier) _(_) _(assembly)(t=0)=x _(carrier) _(_) _(assembly) ⁰  (7)

{dot over (x)} _(rod+spring)(t=0)=0  (8)

{dot over (x)} _(carrier) _(_) _(assembly)(t=0)=0  (9)

The initial positions for the plunger rod 204, the spring 202, andcarrier assembly account for the initial rod and plunger depths as wellas the device activation travel distances. The initial velocities areassumed negligible. These equations are linear and have an analyticsolution:

$\begin{matrix}{{x_{{rod} + {spring}}(t)} = {{\left\lbrack {x_{{rod} + {spring}}^{0} - \left( {L = \frac{F_{friction}}{k}} \right)} \right\rbrack {\cos \left( \sqrt{\frac{k}{M_{{rod} + {spring}}}t} \right)}} + \left( {L - \frac{F_{friction}}{k}} \right)}} & (10) \\{\mspace{20mu} {{x_{{carrier}\; \_ \; {assembly}}(t)} = {{\frac{F_{friction}}{2M_{{carrier}\; \_ \; {assembly}}}t^{2}} + x_{{carrier}\; \_ \; {assembly}}^{0}}}} & (11)\end{matrix}$

The impact time is found by equating the positions of the plunger rod204 and plunger 208 and solving for the impact time. Equation (12) is anon-linear equation for t_(impact), substituting equations (10) and (11)for the respective terms:

x _(rod) _(_) _(+spring)(t _(impact))=x _(carrier) _(_) _(assembly)(t_(impact))  (12)

To solve this non-linear equation iteratively, a reasonable initialvalue for the impact time is required. The frictional force is smallerthan the spring force, so the carrier assembly only translated a smallamount before the first impact. Thus, a good initial value for theimpact time can be found by assuming that the t² term in equation (12),after expanding the right-hand side with equation (11), is negligible.Equation (5) then can be solved exactly, with the form illustrated inequation (13):

$\begin{matrix}{t_{impact} \approx {\sqrt{\frac{M_{{rod} + {spring}}}{k}}{\cos^{- 1}\left\lbrack \frac{x_{{carrier}\; \_ \; {assembly}}^{0} - \left( {L - \frac{F_{friction}}{k}} \right)}{x_{{rod} + {spring}}^{0} - \left( {L - \frac{F_{friction}}{k}} \right)} \right\rbrack}}} & (13)\end{matrix}$

Using equation (13) as an initial estimate, Newton's method can be usedto solve equation (12) numerically. The output of the pre-impactsimulation are the impact time along with the component positions andvelocities at impact:

x _(rod)(t _(impact))  (14)

x _(rod+spring)(t _(impact))  (15)

x _(carrier) _(_) _(assembly)(t _(impact))  (16)

x _(carrier) _(_) _(assembly)(t _(impact))  (17)

Now referring to FIG. 5A, the first impact occurs when the rod 204impacts the plunger 208. FIG. 5B illustrates conceptual separation of asyringe 210 into four components at this pre-impact stage. The plungerrod 204 can be assumed to impact inelastically with the top of theplunger 208-1, which is assumed to contain ¼ of the mass of the plunger208. The remaining mass (component 208-2) is assigned to the syringe210. Throughout the first and second impact, it can be assumed that theplunger rod 204 remains in contact with the top of the plunger 208-1,and that the syringe 210 and the syringe carrier move together at alltimes. Four positions can be tracked in this system, as illustrated inFIG. 5A: the plunger rod button/plunger top (220), the plunger bottom(222), the top of the meniscus (224), and the bottom of the syringe 210(226).

With the exception of the shock tube between meniscus and the syringe210, the forces in the system can be modeled with springs and dashpots,as illustrated in FIG. 5C.

Damping forces are circled in FIG. 5C, and spring forces are notcircled. The spring and syringe driver dry friction forces are the sameas in the previous model, with the dry friction resisting motion betweenthe syringe driver and plunger rod. The internal forces in the syringe210 are modeled as a Voigt elastic. The damping is linear, but thespring force, which can be measured experimentally, can be non-linear.The spring 202 is modeled by including a quadratic term to the standardlinear spring with an equilibrium length. The plunger 208 interacts withthe syringe 210 through direct contact as well as a thin layer of oil,and the interaction is modeled as a linear damping term. When the airgap is included, it is modeled as a spring using an adiabaticcompression approximation. The fluid in the syringe 210 is modeled usingthe Korteweg equations discussed below, along with appropriate boundaryconditions.

With continued reference to FIG. 5C, the resulting forces in the systemare as follows, with velocities denoted with u:

$\begin{matrix}{\mspace{20mu} {F_{srping} = {k\left( {L - x_{rod}} \right)}}} & (18) \\{\mspace{20mu} {F_{{syringe}\; \_ \; {driver}\; \_ \; {damping}} = {{{sign}\left( {u_{{rod}\;} - u_{syringe}} \right)}F_{friction}}}} & (19) \\{F_{{plunger}\; \_ \; {spring}} = {{k_{1}\left( {x_{plunger} - x_{srod} - L_{plunger}} \right)} - {k_{2}\left( {x_{plunger} - x_{rod} - L_{plunger}} \right)}^{2}}} & (20) \\{\mspace{20mu} {F_{{plunger}\; \_ \; {damping}} = {C_{plunger}\left( {u_{rod} - u_{plunger}} \right)}}} & (21) \\{\mspace{20mu} {F_{{syringe}\; \_ \; {friction}} = {C_{syringe}\left( {u_{syringe} - u_{plunger}} \right)}}} & (22) \\{\mspace{20mu} {P_{{air}\; \_ \; {gap}} = {P_{{at}\; m}\left( \frac{H}{x_{mensicus} - x_{plunger}} \right)}^{\gamma}}} & (23) \\{\mspace{20mu} {F_{{air}\; \_ \; {gap}} = {P_{{air}\; \_ \; {gap}}A_{barrel}}}} & (24) \\{\mspace{20mu} {F_{{shock}\; \_ \; {tube}} = {\left( {{P_{{shock}\; \_ \; {tube}}({needle\_ end})} - P_{{at}\; m}} \right)A_{barrel}}}} & (25)\end{matrix}$

The forces are converted into equations of motion using Newton's law,F=ma, once again:

(M _(rod)+⅓M _(spring)+¼M _(plunger)){umlaut over (x)} _(rod) =F_(spring) −F _(syringe) _(_) _(driver) _(_) _(damping) −F _(plunger)_(_) _(spring) −F _(plunger) _(_) _(damping)   (26)

¾M _(plunger) {umlaut over (x)} _(plunger) =F _(plunger) _(_) _(spring)+F _(plunger) _(_) _(damping) −F _(plunger) _(_) _(friction) −F _(air)_(_) _(gap)  (27)

u _(meniscus) =u _(shock) _(_) _(tube)(plunger_end)  (28)

(M _(syringe) ++M _(carrier) +M _(fluid)){umlaut over (x)} _(syringe) =F_(syringe) _(_) _(driver) _(_) _(damping) +F _(plunger) _(_) _(friction)+F _(shock) _(_) _(pressure)  (29)

The initial conditions are specified by applying conservation ofmomentum to the pre-impact output, per equations (14)-(17). The modelalso can be run without an air gap. In this case, F_(air) _(_) _(gap) isreplaced with equation (30):

F _(plunger) _(_) _(shock) =P _(shock) _(_) _(tube)(plunger_end)A_(barrel)  (30)

The fluid pressure in the syringe 210 can be modeled withone-dimensional Korteweg equation, with tracks pressure and velocity asfunctions of axial distance and time:

$\begin{matrix}{\frac{\partial P}{\partial t} = {{- \rho}\; a^{2}\frac{\partial u}{\partial x}}} & (31) \\{\frac{\partial u}{\partial t} = {{- \frac{1}{\rho}}\frac{\partial P}{\partial x}}} & (32)\end{matrix}$

Equations (31) and (32) can be solved with the method ofcharacteristics. The wave speed, a, is calculated with the Kortewegequation (33). The wave speed depends on the speed of sound, densities,and geometries of the fluid and solid systems, as illustrated inequation (34).

$\begin{matrix}{a = \frac{c_{fluid}}{\sqrt{1 + \beta}}} & (33) \\{\beta = {\left( \frac{c_{fluid}}{c_{solid}} \right)^{2}\left( \frac{\rho_{fluid}}{\rho_{solid}} \right)\left( \frac{2R}{h} \right)}} & (34)\end{matrix}$

The tube is broken into N equal elements of size Δx. A time step thencan be selected based on the wave speed and step size.

$\begin{matrix}{{\Delta \; t} = \frac{\Delta \; x}{a}} & (35)\end{matrix}$

At the start of the first impact, the velocity at every node is set tothe syringe velocity output by the pre-impact model of FIGS. 4A and 4B.The pressure is set to atmospheric pressure. At each subsequent timestep, interior notes (excluding the nodes near the plunger and theneedle) are updated with equations (36) and (37):

$\begin{matrix}{{P\left( {x,{t + {\Delta \; t}}} \right)} = {{\frac{1}{2}\left( {{P\left( {{x - {\Delta \; t}},t} \right)} + {P\left( {{x + {\Delta \; t}},t} \right)}} \right)} + {\frac{\rho \; a}{2}\left( {{u\left( {{x - {\Delta \; t}},t} \right)} - {u\left( {{x + {\Delta \; t}},t} \right)}} \right)}}} & (36) \\{{u\left( {x,{t + {\Delta \; t}}} \right)} = {{\frac{1}{2\rho \; a}\left( {{P\left( {{x - {\Delta \; t}},t} \right)} + {P\left( {{x + {\Delta \; t}},t} \right)}} \right)} + {\frac{1}{2}\left( {{u\left( {{x - {\Delta \; t}},t} \right)} + {u\left( {{x + {\Delta \; t}},t} \right)}} \right)}}} & (37)\end{matrix}$

Two possible boundary conditions exist near the needle. In both cases,the boundary node is updated with equation (38):

$\begin{matrix}{{\frac{P\left( {0,{t + {\Delta \; t}}} \right)}{\rho \; a} - {u\left( {0,{t + {\Delta \; t}}} \right)}} = {\frac{P\left( {{\Delta \; x},t} \right)}{\rho \; a} - {u\left( {{\Delta \; x},t} \right)}}} & (38)\end{matrix}$

In both cases, the right-hand side of the equation is known at the startof the time step. If the air gap is present, P(0, t+Δt) is set as theair gap pressure, and the equation is used to solve for the unknownvelocity. If there is no air gap, the velocity on the left-hand side isspecified as the plunger bottom velocity, and the equation solves forthe unknown pressure.

The equation at the needle end is more involved because some fluid isexpelled through the needle. There are two unknowns at the start of atime step: u and P at the needle boundary, so two equations arerequired. The first equation comes from the method of characteristics:

$\begin{matrix}{{\frac{P\left( {L,{t + {\Delta \; t}}} \right)}{\rho \; a} + {u\left( {L,{t + {\Delta \; t}}} \right)}} = {\frac{P\left( {{L - {\Delta \; x}},t} \right)}{\rho \; a} - {u\left( {{L - {\Delta \; x}},t} \right)}}} & (39)\end{matrix}$

The right-hand side is known, while the unknowns appear on the left-handside. The remaining equation is derived by assuming P and u follow theHagen-Poiseuille law:

$\begin{matrix}{{{u\left( {L,{t + {\Delta \; t}}} \right)}A_{barrel}} = {{u_{syringe}A_{barrel}} + {\frac{\pi \; D_{needle}^{4}}{128\mu \; L_{needle}}\left( {{P\left( {L,{t + {\Delta \; t}}} \right)} - P_{{at}\; m}} \right)}}} & (40)\end{matrix}$

Solving both equations simultaneously allows for the update of u and Pat the needle boundary. The syringe velocity appears because theextrusion volume is based on the difference in velocity between theaverage velocity in the shock tube and the velocity of the syringe.

Now referring to FIG. 6A, the second impact is when the carrier contactsa small ledge inside the shell. The equations are identical to firstimpact besides the addition of two new forces, which are circled with anoval in FIG. 6B.

The impact force between the shell and syringe/carrier is modeled with alinear Voigt viscoelastic element. These extra forces are applied to thesyringe:

F _(shell) _(_) _(carrier) _(_) _(spring) =k _(shell) _(_) _(carrier)(x_(syringe) −x _(shell))  (41)

F _(shell) _(_) _(carrier) _(_) _(damping) =C _(shell) _(_) _(carrier) u_(syringe)  (42)

Inputs to the 1D Kinematic Model

Generally speaking, the model 40 discussed above can receive parametersthat specify physical properties of the syringe 120 or 210, theautoinjector 100 or 200, and the drug with which the syringe 120 or 210is pre-filled. These parameters can relate to geometry, friction, mass,viscosity, elasticity, etc. Some of these input parameters are listedbelow. In some embodiments, additional parameters can be used or,conversely, some of the parameters listed below can be omitted. Moreparticularly, in some scenarios, only subsets of the parameters listedbelow can be received, and the remaining parameters can be fixed atcertain constant values or eliminated from the model, depending on theembodiment.

Geometric inputs can include some or all of plunger depth, plunger rodwall thickness, plunger rod activation length, syringe barrel diameter(D_(barrel)), syringe wall thickness (h), fluid volume (V_(fluid)),syringe carrier activation length, plunger rod depth, length of theguide rod, length of guide rod base, length of needle insertion, needlelength (L_(needle)), needle diameter (DM_(needle)), un-sprung length ofspring (L). Input parameters related to mass of various components caninclude one or more of mass of syringe carrier (M_(carrier)), mass ofpre-filled syringe with drug (M_(fluid)+M_(syringe)), mass of plunger,which also may be referred as “plunger-stopper” (M_(plunger)), mass ofrod (M_(rod)), mass of spring (M_(spring)). Visco-elastic inputparameters can include plunger elasticity parameters (k₁ and k₂),plunger plasticity (C_(plunger)), plunger-syringe viscous damping(C_(syringe) _(_) _(friction)), front shell elasticity (k_(shell) _(_)_(carrier)), and front shell damping (C_(shell) _(_) _(carrier)).Fluid-structure interaction (FSI) input parameters can include one ormore of fluid sound speed (c_(fluid)), solid sound speed (c_(solid)),fluid viscosity (μ), fluid density (ρ), solid density for glass(ρ_(solid)). Other parameters can include syringe driver friction(F_(friction)) and spring constant (k).

Alternative Modeling Techniques

As one alternative to the techniques discussed above, a 2D axisymmetricmodel can be constructed, approximating the fluid as an acoustic mediain contact with the syringe through a fluid-structure interaction. Thesolid components can be modeled as linear elastics with an additionalviscous components. Another alternative is a 3D model does not accountfor fluid in the syringe. Experimentation has shown that these 2D and 3Dmodels produce similar results.

However, these large-scale models are not as useful as predictive tools.One reason is, as a result of numerical issues, the models only convergeat low-impact speeds. Long simulation times restrict device explorationin two different device configurations. Further, the models consistentlypredict that the syringe should break in the should region, whereasempirical data shows that the breakage events tend to originate in thecone region.

Moreover, the results for 2D and 3D modeling are heavily dependent onthe penalty parameter used in the contact regions. This parameter is anunphysical numeric value used to keep computational regions frominterpenetrating. Dependence on the results on the penalty parameterindicates that the contact boundary conditions are not capturedaccurately. Also, these models predict extremely high glass stress thatwould shatter most syringes. The empirical data does not support thesepredictions.

Nevertheless, 2D and 3D modeling supports the theory that tensilestresses in the glass, which cause failure, are created by the pressurewaves in the fluid column, that an acoustic model is a suitableapproximation for the fluid column, and that a detailed plunger dynamicshave an insignificant effect on the pressure waves.

As one alternative to the techniques discussed below, a Finite ElementMethod (FEM) can be used to predict peak stress in structural elementsduring impact. However, FEM techniques carry an inherent error and tendto generate a large amount of numerical noise. Moreover, FEM approachesare computationally expensive. Experiments have shown that, whenimplemented on a laptop, the system of FIG. 1 takes only several minutesto model the interaction between an autoinjector, a syringe, and a drugto determine the probability of failure, whereas modeling thisinteraction using a suitable FEM approach takes hours.

In contrast, the speed at which the modeling techniques of thisdisclosure can be executed facilitate the use of Monte Carlo simulation.Generally speaking, Monte Carlo simulation is a powerful technique forexamining the variability of outputs for a given set of inputs withknown variation. Although it is theoretically possible to run MonteCarlo simulations with an FEM technique, this approach is impractical,as Monte Carlo simulations are prone to difficulties with convergingacross a wide range of inputs.

It is also noted that the model 40 predicts peak pressure in thesyringe, which can be directly measured to drive the model 40 toaccuracy, whereas a typical FEM predicts stress. Stress is an inferredproperty, and as such cannot be measured directly.

Application of Experimental Data to Models

In an embodiment, the model 40 uses several damping constants that arederived from experimental (empirical) data. For example, high-speedvideo capturing techniques can be used to measure rod velocity, syringevelocity, pressure, etc. at multiple times for a certain autoinjector.The experiments can be repeated multiple times to generate a reliabledata sample. The system 10 then can store the data sample in thehistorical database 22, for example (see FIG. 1). Subsequently, thesystem 10 can utilize parameters derived from experimental data to modelautoinjectors that share some of the properties of the actualautoinjector. In an example embodiment, the model 40 uses the followingdamping constants: (i) syringe driver friction, which is the frictionbetween the syringe driver and the plunger rod, (ii) internal plungerdamping, (iii) plunger-syringe friction, and (iv) the shell dampingconstant.

Referring to FIG. 7, the power pack of a certain actual autoinjector canbe tested without a syringe, a syringe carrier, a front shell, etc. toproduce a graph 300, in which data points illustrate measurements of rodvelocity as a function of time (the “velocity trace”). In this example,the plot is an average of ten runs. The velocity trace then can becompared with the analytical predictions of the pre-impact model (seeFIGS. 4A and 4B), and the plunger syringe friction can be fit with leastsquares. In FIG. 7, line 302 illustrates the theoretical predictionafter fitting the syringe driver friction. Syringe driver friction canbe evaluated for each individual spring/power pack combination, as thethis parameter can vary significantly across different configurations ofan autoinjector.

After fitting the pre-impact model, internal plunger damping andplunger-syringe friction appear in the first-impact model (see FIGS.5A-5C) as new parameters. To fit internal plunger damping, peakfirst-impact pressure can be measured over a range of impact velocities.As illustrated in graph 310 of FIG. 8, the relationship is approximatelylinear over a wide range of impact velocities. Experiments show that theair gap between the plunger and meniscus has a relatively weak effect onthe peak pressure measurements. In the air gap model, the singularity inthe adiabatic approximation can cause an unrealistically large peakpressure and a nonlinear relationship between impact speed and pressure,as the actual impact causes air to entrain within the drug. Accordingly,the air gap can be removed from all simulations used to predict peakpressures. This results in a more physically accurate simplification. Aleast squares fit 312 can be used to determine plunger damping.

Regarding plunger-syringe friction, this parameter is heavily dependenton the syringe siliconization and individual plunger configuration. Asillustrated in FIG. 9, this parameter can be fit by comparing high-speedvideo traces of the rod 320 and syringe velocity 322 immediately afterfirst impact but before second impact. The model rod and model syringecurves are 326 and 328, respectively. Although the air gap has anegligible impact on the peak pressure, it tends to have a strong effecton the velocity trace after first impact. Thus, an air gap can bereintroduced for this series of simulations. The plunger-syringefriction can be fit, manually or automatically, to the data in graph320.

Finally, the shell damping constant can be derived from second-impactmeasurements. In the model 40, the second impact peak force is directlyrelated to the impact velocity with proportionality constant equivalentto the shell damping constant. Thus, the damping constant can be readoff the slope of line 330 in FIG. 1, which illustrates the relationshipbetween peak force and impact velocity.

In an example embodiment, the parameter selection module 50automatically determines the damping constants (i)-(iv) usingexperimental data stored in the historical database 22 and stores theresults in the parameter database 20. In other embodiments, some or allof the damping constants (i)-(iv) can be determined separately and inputinto the model 40 via user interface controls provided by the parameterselection module 50. For example, an operator can choose to input someof the values manually.

Using Models in Monte Carlo Simulations

As discussed above, the main outputs of the model 40 are the peakpressures experienced at the first and second impacts for the variousconfigurations of interest. Monte Carlo simulations can be conducted topredict both the average peak pressures as well as the ranges likely tobe seen in the field, i.e., when the autoinjector being modeled ismanufactured.

There are four steps in a general Monte Carlo simulation: (i) a domainof possible inputs is defined (in these simulations, the inputs arespring forces, plunger depth, etc.); (ii) inputs are generated randomlyfrom a probability distribution (in these simulations, a normal randomvariable with a measured mean and standard deviation for each inputparameter is used), (iii) deterministic computations are run for allgenerated input sets; and (iv) the results are aggregates of peakpressures for the first and second impacts. For each candidateconfiguration, average values can be measured for every input parameter,and standard deviations can be measured or approximated. In eachsimulation, parameters can be drawn from normal distributions withcorresponding means and standard deviations. A sample distribution 340is illustrated in FIG. 11. This distribution is based on the model 40producing one hundred independent simulations, in each of which a peakpressure was recorded. For this simulation, a nominal plunger depth of10.5 mm was used.

The same distribution 340 illustrates that, first, average peak pressureis significantly higher for second impact at the plunger depths selectedfor the simulation. Second, the standard deviation for the first impactpeak pressure is higher than second impact. Experimentation shows thatthis is chiefly a result of the power pack variability. Finally, thedistributions can be reasonably approximated as normal, so eachdistribution can be accurately specified using the mean and standarddeviation. Multiple experiments have been conducted, and all Monte Carlosimulations showed similarly normal distributions.

Using Models with Taguchi Methods

Another possible application of the model 40 discussed above is using atwo-level Taguchi method to explore the design space of the range ofautoinjectors. Taguchi is a specific form of a Design of Experimentsmethodology used to identify the strongest influencing variables in amulti-variable space (Design of Experiments is a set of methods used toidentify experimental selection and sequence to maximize the value ofinformation generated). A high and low value can be identified for asubset of the input variables. A set of N simulations can be designed,such that every pair of parameters is combined in all four possible ways(low-low, low-high, high-low, and high-high).

The peak pressures can be modeled for all N simulations. Based on theresults, a signal-to-noise (SNR) value can be calculated for eachexperiment. For each parameter, the average value of the SNR can becalculated separately for the simulations with a low parameter value andthe simulations with a high parameter value. The difference (Δ) betweenSNR values (the low set of simulations compared with the high set ofsimulations) indicates the significance of each parameter on the peakpressures. Larger absolute values for Δ are associated with moreimportant parameters.

For example, after N runs, the output of a Taguchi method for the model40 can be a first Δ value for the spring constant, generated for thefirst impact, and a second Δ value for the spring constant, generatedfor the second impact. For an example configuration of an autoinjectorbeing modeled, relatively large Δ values for the spring constantindicate that the spring constant is a significant parameter for thefirst impact as well as the second impact. However, a first Δ value anda second Δ value can be similarly produced for the spring lengthparameter for the first impact and the second impact, respectively, anda relatively small first Δ value can indicate that the spring length isnot a significant parameter for the first impact but is a significantparameter for the second impact. As yet another example, a first Δ valueand a second Δ value can be produced for the parameter specifying therod activation distance. Both the first Δ value and the second Δ valuecan be relatively small, indicating that this parameter is notsignificant for either the first impact or the second impact.

Referring back to FIG. 1, the modeling system 30 can provide appropriateUI controls for selecting N, specifying parameters for Taguchi methodruns, displaying and tabulating the Δ values, etc. The modeling system30 can implement the Taguchi functionality in the parameter selectionmodule 50, for example.

Glass Breakage Impact Characterization

The probability of failure calculation module 60 can use the two-termWeibull distribution because this approaches yields more accuratepredictions, particularly at the end of the “long tail.” This isespecially useful when modeling autoinjectors that tend to deliverhigh-viscosity drugs. However, in other implementations other techniquescan be used, such as using a logistic fit function, a log-logistic fitfunction, a spline fit function, or a Gaussian fit function.

Generally speaking, glass breakage occurs when stress is applied to acritical surface defect size on the glass. The term “defect” here refersto a micro-scale geometric variation that meets manufacturingspecification, and is generally not detectable by current productionmethods. Needle cone surfaces are free-formed, and thus these defectsare inherent to syringe formation. The origination of the glass fractureoccurs where the largest stress is applied to the largest surface flaw.This can be referred to as the “weakest link” phenomena. The stress inthe glass can be expressed by the relationship in equation (43):

δ=K _(c) ×P  (43)

Example data collected from a characterization study shows behaviorindicative of an exponential rise followed by an exponential decay withthe inflection point at a certain breakage probability (e.g., 50%). Thisobservation and the “weakest link” phenomena basis for glass fracturelead to a Weibull two parameter distribution fit to the data followingequation (44):

$\begin{matrix}{P_{f} = {1 - {\exp \left( {- \left( \frac{\delta}{\delta_{0}} \right)^{m}} \right)}}} & (44)\end{matrix}$

The probability of glass breakage (P_(f)) is a function of local stress(σ), surface geometry (σ_(O)), and glass surface quality (m). Thisapproach uses peak pressure as a surrogate for stress since stresscannot be measured directly within the syringe. Equation (43)demonstrates that stress is directly proportional to pressure (P)assuming a random distribution of surface flaws with concentrationfactor (K_(c)).

The probability of failure calculation module 60 then can extrapolatethe fit to the observed pressures delivered by the drug delivery deviceand use the extrapolated fit to predict probability of glass breakagewith different configurations of the drug delivery device. For example,the probability of failure calculation module 60 can predictprobabilities of glass breakage within the syringe 120 (see FIGS. 2A-3F)for different sets of parameters of the autoinjector 100, such as thespring constant, the mass of the syringe, the density of the drug, etc.

In an embodiment, the estimation in the glass breakage predictionuncertainty is divided into three components: (i) statistical samplinguncertainty (based on a percent of the absolute value), (ii) measurementuncertainly (based on a percent of the absolute value), and (iii) fitbias compared to actual field data (based on low and high bias). The fitbias can be based purely on the absolute value difference between theprediction and the field-reported value.

Example Methods

FIG. 12 is a flow diagram of an example method for determining predictedfailure rates of drug injection devices. The method can be implementedin the modeling system 30, for example. More generally, the method 400can be implemented as a set of instructions stored on a non-transitorycomputer-readable medium and executable on one or more processors.

The method 400 begins at block 402, where parameters for a druginjection device are received. At blocks 404 and 406, parameters for asyringe and a drug, respectively, are received. As discussed above,these parameters can include geometric inputs related to the plunger,plunger depth, the syringe, spring length, etc.; mass parameters relatedto the syringe, the plunger, the spring, etc.; visco-elastic inputparameters; etc.

Some or all of these parameters can be received via the user interfaceof the parameter selection module 50. Some parameters, such as dampingconstants, can be derived using experimental data as discussed above.Further, in some scenarios, some of the input parameters are generatedautomatically in an iterative manner so as to generate and subsequentlycompare respective outputs. For example, the parameter selection module50 can iterate through multiple values of the plunger depth in a certainrange [D₁, D₂], with a step S, while keeping the other parameters thesame (or adjusted only in view of the change to the plunger depth). Theinjector modeling module 32 can generate respective predicted peakpressure values for each value of the plunger depth and determine whichvalues produce acceptable results, which values produce optimal results,etc. If desired, the parameter selection module 50 can automaticallyadjust multiple parameters at the same time when seeking an acceptableset of configuration parameters.

With continued reference to FIG. 12, the received parameters are appliedto the model to generate a predicted pressures at block 408. Next, atblock 410, experimental (empirical) data for peak pressures arereceived. Generally speaking, the experimental values can be obtained inany suitable manner, and can vary in quality depending on the number ofsamples tested, how well the parameters of the tested devices correspondto the input parameters into the model, etc.

The probability of failure is determined at block 412 using predictedpeak pressure output by the model and the empirical data received atblock 410. To this end, the two-term Weibull distribution, or anothersuitable statistical technique, can be applied.

Next, at block 414, an indication of the determine probability offailure is provided to a user via a user interface, or the determinedprobability of failure can be used in an automated process to modify oneor several parameters and re-apply the parameters to the model. Thelatter approach is discussed in more detail below with reference to FIG.13.

Now referring to FIG. 13, a method 450 also can be implemented in themodeling system 30 as a set of instructions stored on a non-transitorycomputer-readable medium and executable on one or more processors. Themethod 450 is applicable to drug injection devices such as theautoinjector 100 discussed above.

The method 450 begins at block 452, where a set of “fixed” parametersare received. For example, an operator using the system 30 can decide tofix the parameters of the syringe and the drug for various businessreasons, and decide to vary only the parameters of the drug injectiondevice. Of course, the operator can also fix some of the parameters ofthe drug injection device (or at least impose certain narrowrestrictions on these parameters, such as small ranges of permissiblevalues).

At block 454, a candidate set of parameters for the drug injectiondevice is received. Some of these parameters may be generatedautomatically. At block 456, the parameters obtained at block 452 and454 are applied to the 1D kinematic model to generate peak pressure, andprobability of failure is determined using the predicted peak pressureand empirical data at block 458 (similar to the method 400 discussedabove).

The resulting probability is then compared to a certain threshold valueat block 460. If the probability is determined to be acceptable, theflow proceeds to block 462, where the set of parameters applied to themodel is selected as an acceptable configuration. Otherwise, if theprobability is determined to exceed the threshold and accordingly deemedunacceptable, the flow returns to block 454, where a new set ofcandidate parameters is generated (or received from an operator, in analternative scenario).

More particularly, as a result of executing block 462, improvementactions can be initiated. For example, the design of the autoinjectorcan be modified to reduce pressure within the syringe. According to oneexample scenario, a different needle can be used to reduce the requiredextrusion force of the drug, which in turn permits using a lower-forcespring. The method completes after executing block 462.

Additional Considerations

It should be understood that the above-described techniques can be usedwith various devices that deliver, or utilize in operation,high-viscosity liquids. These devices include but are not limited toauto-injectors, and the high-viscosity liquids include but are notlimited to drugs. Thus, although

The above description describes various systems and methods for use witha drug delivery device. It should be clear that the system, drugdelivery device or methods can further comprise use of a medicamentlisted below with the caveat that the following list should neither beconsidered to be all inclusive nor limiting. The medicament will becontained in a reservoir. In some instances, the reservoir is a primarycontainer that is either filled or pre-filled for treatment with themedicament. The primary container can be a cartridge or a pre-filledsyringe.

For example, the drug delivery device or more specifically the reservoirof the device may be filled with colony stimulating factors, such asgranulocyte colony-stimulating factor (G-CSF). Such G-CSF agentsinclude, but are not limited to, Neupogen® (filgrastim) and Neulasta®(pegfilgrastim). In various other embodiments, the drug delivery devicemay be used with various pharmaceutical products, such as anerythropoiesis stimulating agent (ESA), which may be in a liquid or alyophilized form. An ESA is any molecule that stimulates erythropoiesis,such as Epogen® (epoetin alfa), Aranesp® (darbepoetin alfa), Dynepo®(epoetin delta), Mircera® (methyoxy polyethylene glycol-epoetin beta),Hematide®, MRK-2578, INS-22, Retacrit® (epoetin zeta), Neorecormon®(epoetin beta), Silapo® (epoetin zeta), Binocrit® (epoetin alfa),epoetin alfa Hexal, Abseamed® (epoetin alfa), Ratioepo® (epoetin theta),Eporatio® (epoetin theta), Biopoin® (epoetin theta), epoetin alfa,epoetin beta, epoetin zeta, epoetin theta, and epoetin delta, as well asthe molecules or variants or analogs thereof as disclosed in thefollowing patents or patent applications, each of which is hereinincorporated by reference in its entirety: U.S. Pat. Nos. 4,703,008;5,441,868; 5,547,933; 5,618,698; 5,621,080; 5,756,349; 5,767,078;5,773,569; 5,955,422; 5,986,047; 6,583,272; 7,084,245; and 7,271,689;and PCT Publication Nos. WO 91/05867; WO 95/05465; WO 96/40772; WO00/24893; WO 01/81405; and WO 2007/136752.

An ESA can be an erythropoiesis stimulating protein. As used herein,“erythropoiesis stimulating protein” means any protein that directly orindirectly causes activation of the erythropoietin receptor, forexample, by binding to and causing dimerization of the receptor.Erythropoiesis stimulating proteins include erythropoietin and variants,analogs, or derivatives thereof that bind to and activate erythropoietinreceptor; antibodies that bind to erythropoietin receptor and activatethe receptor; or peptides that bind to and activate erythropoietinreceptor. Erythropoiesis stimulating proteins include, but are notlimited to, epoetin alfa, epoetin beta, epoetin delta, epoetin omega,epoetin iota, epoetin zeta, and analogs thereof, pegylatederythropoietin, carbamylated erythropoietin, mimetic peptides (includingEMP1/hematide), and mimetic antibodies. Exemplary erythropoiesisstimulating proteins include erythropoietin, darbepoetin, erythropoietinagonist variants, and peptides or antibodies that bind and activateerythropoietin receptor (and include compounds reported in U.S.Publication Nos. 2003/0215444 and 2006/0040858, the disclosures of eachof which is incorporated herein by reference in its entirety) as well aserythropoietin molecules or variants or analogs thereof as disclosed inthe following patents or patent applications, which are each hereinincorporated by reference in its entirety: U.S. Pat. Nos. 4,703,008;5,441,868; 5,547,933; 5,618,698; 5,621,080; 5,756,349; 5,767,078;5,773,569; 5,955,422; 5,830,851; 5,856,298; 5,986,047; 6,030,086;6,310,078; 6,391,633; 6,583,272; 6,586,398; 6,900,292; 6,750,369;7,030,226; 7,084,245; and 7,217,689; U.S. Publication Nos. 2002/0155998;2003/0077753; 2003/0082749; 2003/0143202; 2004/0009902; 2004/0071694;2004/0091961; 2004/0143857; 2004/0157293; 2004/0175379; 2004/0175824;2004/0229318; 2004/0248815; 2004/0266690; 2005/0019914; 2005/0026834;2005/0096461; 2005/0107297; 2005/0107591; 2005/0124045; 2005/0124564;2005/0137329; 2005/0142642; 2005/0143292; 2005/0153879; 2005/0158822;2005/0158832; 2005/0170457; 2005/0181359; 2005/0181482; 2005/0192211;2005/0202538; 2005/0227289; 2005/0244409; 2006/0088906; and2006/0111279; and PCT Publication Nos. WO 91/05867; WO 95/05465; WO99/66054; WO 00/24893; WO 01/81405; WO 00/61637; WO 01/36489; WO02/014356; WO 02/19963; WO 02/20034; WO 02/49673; WO 02/085940; WO03/029291; WO 2003/055526; WO 2003/084477; WO 2003/094858; WO2004/002417; WO 2004/002424; WO 2004/009627; WO 2004/024761; WO2004/033651; WO 2004/035603; WO 2004/043382; WO 2004/101600; WO2004/101606; WO 2004/101611; WO 2004/106373; WO 2004/018667; WO2005/001025; WO 2005/001136; WO 2005/021579; WO 2005/025606; WO2005/032460; WO 2005/051327; WO 2005/063808; WO 2005/063809; WO2005/070451; WO 2005/081687; WO 2005/084711; WO 2005/103076; WO2005/100403; WO 2005/092369; WO 2006/50959; WO 2006/02646; and WO2006/29094.

Examples of other pharmaceutical products for use with the device mayinclude, but are not limited to, antibodies such as Vectibix®(panitumumab), Xgeva™ (denosumab) and Prolia™ (denosamab); otherbiological agents such as Enbrel® (etanercept, TNF-receptor/Fc fusionprotein, TNF blocker), Neulasta® (pegfilgrastim, pegylated filgastrim,pegylated G-CSF, pegylated hu-Met-G-CSF), Neupogen® (filgrastim, G-CSF,hu-MetG-CSF), and Nplate® (romiplostim); small molecule drugs such asSensipar® (cinacalcet). The device may also be used with a therapeuticantibody, a polypeptide, a protein or other chemical, such as an iron,for example, ferumoxytol, iron dextrans, ferric glyconate, and ironsucrose. The pharmaceutical product may be in liquid form, orreconstituted from lyophilized form.

Among particular illustrative proteins are the specific proteins setforth below, including fusions, fragments, analogs, variants orderivatives thereof:

OPGL specific antibodies, peptibodies, and related proteins, and thelike (also referred to as RANKL specific antibodies, peptibodies and thelike), including fully humanized and human OPGL specific antibodies,particularly fully humanized monoclonal antibodies, including but notlimited to the antibodies described in PCT Publication No. WO 03/002713,which is incorporated herein in its entirety as to OPGL specificantibodies and antibody related proteins, particularly those having thesequences set forth therein, particularly, but not limited to, thosedenoted therein: 9H7; 18B2; 2D8; 2E11; 16E1; and 22B3, including theOPGL specific antibodies having either the light chain of SEQ ID NO:2 asset forth therein in FIG. 2 and/or the heavy chain of SEQ ID NO:4, asset forth therein in FIG. 4, each of which is individually andspecifically incorporated by reference herein in its entirety fully asdisclosed in the foregoing publication;

Myostatin binding proteins, peptibodies, and related proteins, and thelike, including myostatin specific peptibodies, particularly thosedescribed in U.S. Publication No. 2004/0181033 and PCT Publication No.WO 2004/058988, which are incorporated by reference herein in theirentirety particularly in parts pertinent to myostatin specificpeptibodies, including but not limited to peptibodies of the mTN8-19family, including those of SEQ ID NOS:305-351, including TN8-19-1through TN8-19-40, TN8-19 con1 and TN8-19 con2; peptibodies of the mL2family of SEQ ID NOS:357-383; the mL15 family of SEQ ID NOS:384-409; themL17 family of SEQ ID NOS:410-438; the mL20 family of SEQ IDNOS:439-446; the mL21 family of SEQ ID NOS:447-452; the mL24 family ofSEQ ID NOS:453-454; and those of SEQ ID NOS:615-631, each of which isindividually and specifically incorporated by reference herein in theirentirety fully as disclosed in the foregoing publication;

IL-4 receptor specific antibodies, peptibodies, and related proteins,and the like, particularly those that inhibit activities mediated bybinding of IL-4 and/or IL-13 to the receptor, including those describedin PCT Publication No. WO 2005/047331 or PCT Application No.PCT/US2004/37242 and in U.S. Publication No. 2005/112694, which areincorporated herein by reference in their entirety particularly in partspertinent to IL-4 receptor specific antibodies, particularly suchantibodies as are described therein, particularly, and withoutlimitation, those designated therein: L1H1; L1H2; L1H3; L1H4; L1H5;L1H6; L1H7; L1H8; L1H9; L1H10; L1H11; L2H1; L2H2; L2H3; L2H4; L2H5;L2H6; L2H7; L2H8; L2H9; L2H10; L2H11; L2H12; L2H13; L2H14; L3H1; L4H1;L5H1; L6H1, each of which is individually and specifically incorporatedby reference herein in its entirety fully as disclosed in the foregoingpublication;

Interleukin 1-receptor 1 (“IL1-R1”) specific antibodies, peptibodies,and related proteins, and the like, including but not limited to thosedescribed in U.S. Publication No. 2004/097712, which is incorporatedherein by reference in its entirety in parts pertinent to IL1-R1specific binding proteins, monoclonal antibodies in particular,especially, without limitation, those designated therein: 15CA, 26F5,27F2, 24E12, and 10H7, each of which is individually and specificallyincorporated by reference herein in its entirety fully as disclosed inthe aforementioned publication;

Ang2 specific antibodies, peptibodies, and related proteins, and thelike, including but not limited to those described in PCT PublicationNo. WO 03/057134 and U.S. Publication No. 2003/0229023, each of which isincorporated herein by reference in its entirety particularly in partspertinent to Ang2 specific antibodies and peptibodies and the like,especially those of sequences described therein and including but notlimited to: L1(N); L1(N) WT; L1(N) 1K WT; 2×L1(N); 2×L1(N) WT; Con4 (N),Con4 (N) 1K WT, 2×Con4 (N) 1K; L1C; L1C 1K; 2×L1C; Con4C; Con4C 1K;2×Con4C 1K; Con4-L1 (N); Con4-L1C; TN-12-9 (N); C17 (N); TN8-8(N);TN8-14 (N); Con 1 (N), also including anti-Ang 2 antibodies andformulations such as those described in PCT Publication No. WO2003/030833 which is incorporated herein by reference in its entirety asto the same, particularly Ab526; Ab528; Ab531; Ab533; Ab535; Ab536;Ab537; Ab540; Ab543; Ab544; Ab545; Ab546; A551; Ab553; Ab555; Ab558;Ab559; Ab565; AbF1AbFD; AbFE; AbFJ; AbFK; AbG1D4; AbGC1E8; AbH1C12;Ab1A1; Ab1F; Ab1K, Ab1P; and Ab1P, in their various permutations asdescribed therein, each of which is individually and specificallyincorporated by reference herein in its entirety fully as disclosed inthe foregoing publication;

NGF specific antibodies, peptibodies, and related proteins, and the likeincluding, in particular, but not limited to those described in U.S.Publication No. 2005/0074821 and U.S. Pat. No. 6,919,426, which areincorporated herein by reference in their entirety particularly as toNGF-specific antibodies and related proteins in this regard, includingin particular, but not limited to, the NGF-specific antibodies thereindesignated 4D4, 4G6, 6H9, 7H2, 14D10 and 14D11, each of which isindividually and specifically incorporated by reference herein in itsentirety fully as disclosed in the foregoing publication;

CD22 specific antibodies, peptibodies, and related proteins, and thelike, such as those described in U.S. Pat. No. 5,789,554, which isincorporated herein by reference in its entirety as to CD22 specificantibodies and related proteins, particularly human CD22 specificantibodies, such as but not limited to humanized and fully humanantibodies, including but not limited to humanized and fully humanmonoclonal antibodies, particularly including but not limited to humanCD22 specific IgG antibodies, such as, for instance, a dimer of ahuman-mouse monoclonal hLL2 gamma-chain disulfide linked to ahuman-mouse monoclonal hLL2 kappa-chain, including, but limited to, forexample, the human CD22 specific fully humanized antibody inEpratuzumab, CAS registry number 501423-23-0;

IGF-1 receptor specific antibodies, peptibodies, and related proteins,and the like, such as those described in PCT Publication No. WO06/069202, which is incorporated herein by reference in its entirety asto IGF-1 receptor specific antibodies and related proteins, includingbut not limited to the IGF-1 specific antibodies therein designatedL1H1, L2H2, L3H3, L4H4, L5H5, L6H6, L7H7, L8H8, L9H9, L10H10, L11H11,L12H12, L13H13, L14H14, L15H15, L16H16, L17H17, L18H18, L19H19, L20H20,L21H21, L22H22, L23H23, L24H24, L25H25, L26H26, L27H27, L28H28, L29H29,L30H30, L31H31, L32H32, L33H33, L34H34, L35H35, L36H36, L37H37, L38H38,L39H39, L40H40, L41H41, L42H42, L43H43, L44H44, L45H45, L46H46, L47H47,L48H48, L49H49, L50H50, L51H51, L52H52, and IGF-1R-binding fragments andderivatives thereof, each of which is individually and specificallyincorporated by reference herein in its entirety fully as disclosed inthe foregoing publication;

Also among non-limiting examples of anti-IGF-1R antibodies for use inthe methods and compositions of the present invention are each and allof those described in:

(i) U.S. Publication No. 2006/0040358 (published Feb. 23, 2006),2005/0008642 (published Jan. 13, 2005), 2004/0228859 (published Nov. 18,2004), including but not limited to, for instance, antibody 1A (DSMZDeposit No. DSM ACC 2586), antibody 8 (DSMZ Deposit No. DSM ACC 2589),antibody 23 (DSMZ Deposit No. DSM ACC 2588) and antibody 18 as describedtherein;

(ii) PCT Publication No. WO 06/138729 (published Dec. 28, 2006) and WO05/016970 (published Feb. 24, 2005), and Lu et al. (2004), J. Biol.Chem. 279:2856-2865, including but not limited to antibodies 2F8, A12,and IMC-A12 as described therein;

(iii) PCT Publication No. WO 07/012614 (published Feb. 1, 2007), WO07/000328 (published Jan. 4, 2007), WO 06/013472 (published Feb. 9,2006), WO 05/058967 (published Jun. 30, 2005), and WO 03/059951(published Jul. 24, 2003);

(iv) U.S. Publication No. 2005/0084906 (published Apr. 21, 2005),including but not limited to antibody 7C10, chimaeric antibody C7C10,antibody h7C10, antibody 7H2M, chimaeric antibody *7C10, antibody GM607, humanized antibody 7C10 version 1, humanized antibody 7C10 version2, humanized antibody 7C10 version 3, and antibody 7H2HM, as describedtherein;

(v) U.S. Publication Nos. 2005/0249728 (published Nov. 10, 2005),2005/0186203 (published Aug. 25, 2005), 2004/0265307 (published Dec. 30,2004), and 2003/0235582 (published Dec. 25, 2003) and Maloney et al.(2003), Cancer Res. 63:5073-5083, including but not limited to antibodyEM164, resurfaced EM164, humanized EM164, huEM164 v1.0, huEM164 v1.1,huEM164 v1.2, and huEM164 v1.3 as described therein;

(vi) U.S. Pat. No. 7,037,498 (issued May 2, 2006), U.S. Publication Nos.2005/0244408 (published Nov. 30, 2005) and 2004/0086503 (published May6, 2004), and Cohen, et al. (2005), Clinical Cancer Res. 11:2063-2073,e.g., antibody CP-751,871, including but not limited to each of theantibodies produced by the hybridomas having the ATCC accession numbersPTA-2792, PTA-2788, PTA-2790, PTA-2791, PTA-2789, PTA-2793, andantibodies 2.12.1, 2.13.2, 2.14.3, 3.1.1, 4.9.2, and 4.17.3, asdescribed therein;

(vii) U.S. Publication Nos. 2005/0136063 (published Jun. 23, 2005) and2004/0018191 (published Jan. 29, 2004), including but not limited toantibody 19D12 and an antibody comprising a heavy chain encoded by apolynucleotide in plasmid 15H12/19D12 HCA (γ4), deposited at the ATCCunder number PTA-5214, and a light chain encoded by a polynucleotide inplasmid 15H12/19D12 LCF (κ), deposited at the ATCC under numberPTA-5220, as described therein; and

(viii) U.S. Publication No. 2004/0202655 (published Oct. 14, 2004),including but not limited to antibodies PINT-6A1, PINT-7A2, PINT-7A4,PINT-7A5, PINT-7A6, PINT-8A1, PINT-9A2, PINT-11A1, PINT-11A2, PINT-11A3,PINT-11A4, PINT-11A5, PINT-11A7, PINT-11A12, PINT-12A1, PINT-12A2,PINT-12A3, PINT-12A4, and PINT-12A5, as described therein; each and allof which are herein incorporated by reference in their entireties,particularly as to the aforementioned antibodies, peptibodies, andrelated proteins and the like that target IGF-1 receptors;

B-7 related protein 1 specific antibodies, peptibodies, related proteinsand the like (“B7RP-1,” also is referred to in the literature as B7H2,ICOSL, B7h, and CD275), particularly B7RP-specific fully humanmonoclonal IgG2 antibodies, particularly fully human IgG2 monoclonalantibody that binds an epitope in the first immunoglobulin-like domainof B7RP-1, especially those that inhibit the interaction of B7RP-1 withits natural receptor, ICOS, on activated T cells in particular,especially, in all of the foregoing regards, those disclosed in U.S.Publication No. 2008/0166352 and PCT Publication No. WO 07/011941, whichare incorporated herein by reference in their entireties as to suchantibodies and related proteins, including but not limited to antibodiesdesignated therein as follow: 16H (having light chain variable and heavychain variable sequences SEQ ID NO:1 and SEQ ID NO:7 respectivelytherein); 5D (having light chain variable and heavy chain variablesequences SEQ ID NO:2 and SEQ ID NO:9 respectively therein); 2H (havinglight chain variable and heavy chain variable sequences SEQ ID NO:3 andSEQ ID NO:10 respectively therein); 43H (having light chain variable andheavy chain variable sequences SEQ ID NO:6 and SEQ ID NO:14 respectivelytherein); 41H (having light chain variable and heavy chain variablesequences SEQ ID NO:5 and SEQ ID NO:13 respectively therein); and 15H(having light chain variable and heavy chain variable sequences SEQ IDNO:4 and SEQ ID NO:12 respectively therein), each of which isindividually and specifically incorporated by reference herein in itsentirety fully as disclosed in the foregoing publication;

IL-15 specific antibodies, peptibodies, and related proteins, and thelike, such as, in particular, humanized monoclonal antibodies,particularly antibodies such as those disclosed in U. S. PublicationNos. 2003/0138421; 2003/023586; and 2004/0071702; and U.S. Pat. No.7,153,507, each of which is incorporated herein by reference in itsentirety as to IL-15 specific antibodies and related proteins, includingpeptibodies, including particularly, for instance, but not limited to,HuMax IL-15 antibodies and related proteins, such as, for instance,146B7;

IFN gamma specific antibodies, peptibodies, and related proteins and thelike, especially human IFN gamma specific antibodies, particularly fullyhuman anti-IFN gamma antibodies, such as, for instance, those describedin U.S. Publication No. 2005/0004353, which is incorporated herein byreference in its entirety as to IFN gamma specific antibodies,particularly, for example, the antibodies therein designated 1118;1118*; 1119; 1121; and 1121*. The entire sequences of the heavy andlight chains of each of these antibodies, as well as the sequences oftheir heavy and light chain variable regions and complementaritydetermining regions, are each individually and specifically incorporatedby reference herein in its entirety fully as disclosed in the foregoingpublication and in Thakur et al. (1999), Mol. Immunol. 36:1107-1115. Inaddition, description of the properties of these antibodies provided inthe foregoing publication is also incorporated by reference herein inits entirety. Specific antibodies include those having the heavy chainof SEQ ID NO:17 and the light chain of SEQ ID NO:18; those having theheavy chain variable region of SEQ ID NO:6 and the light chain variableregion of SEQ ID NO:8; those having the heavy chain of SEQ ID NO:19 andthe light chain of SEQ ID NO:20; those having the heavy chain variableregion of SEQ ID NO:10 and the light chain variable region of SEQ IDNO:12; those having the heavy chain of SEQ ID NO:32 and the light chainof SEQ ID NO:20; those having the heavy chain variable region of SEQ IDNO:30 and the light chain variable region of SEQ ID NO:12; those havingthe heavy chain sequence of SEQ ID NO:21 and the light chain sequence ofSEQ ID NO:22; those having the heavy chain variable region of SEQ IDNO:14 and the light chain variable region of SEQ ID NO:16; those havingthe heavy chain of SEQ ID NO:21 and the light chain of SEQ ID NO:33; andthose having the heavy chain variable region of SEQ ID NO:14 and thelight chain variable region of SEQ ID NO:31, as disclosed in theforegoing publication. A specific antibody contemplated is antibody 1119as disclosed in the foregoing U.S. publication and having a completeheavy chain of SEQ ID NO:17 as disclosed therein and having a completelight chain of SEQ ID NO:18 as disclosed therein;

TALL-1 specific antibodies, peptibodies, and the related proteins, andthe like, and other TALL specific binding proteins, such as thosedescribed in U.S. Publication Nos. 2003/0195156 and 2006/0135431, eachof which is incorporated herein by reference in its entirety as toTALL-1 binding proteins, particularly the molecules of Tables 4 and 5B,each of which is individually and specifically incorporated by referenceherein in its entirety fully as disclosed in the foregoing publications;

Parathyroid hormone (“PTH”) specific antibodies, peptibodies, andrelated proteins, and the like, such as those described in U.S. Pat. No.6,756,480, which is incorporated herein by reference in its entirety,particularly in parts pertinent to proteins that bind PTH;

Thrombopoietin receptor (“TPO-R”) specific antibodies, peptibodies, andrelated proteins, and the like, such as those described in U.S. Pat. No.6,835,809, which is herein incorporated by reference in its entirety,particularly in parts pertinent to proteins that bind TPO-R;

Hepatocyte growth factor (“HGF”) specific antibodies, peptibodies, andrelated proteins, and the like, including those that target theHGF/SF:cMet axis (HGF/SF:c-Met), such as the fully human monoclonalantibodies that neutralize hepatocyte growth factor/scatter (HGF/SF)described in U.S. Publication No. 2005/0118643 and PCT Publication No.WO 2005/017107, huL2G7 described in U.S. Pat. No. 7,220,410 and OA-5d5described in U.S. Pat. Nos. 5,686,292 and 6,468,529 and in PCTPublication No. WO 96/38557, each of which is incorporated herein byreference in its entirety, particularly in parts pertinent to proteinsthat bind HGF;

TRAIL-R2 specific antibodies, peptibodies, related proteins and thelike, such as those described in U.S. Pat. No. 7,521,048, which isherein incorporated by reference in its entirety, particularly in partspertinent to proteins that bind TRAIL-R2;

Activin A specific antibodies, peptibodies, related proteins, and thelike, including but not limited to those described in U.S. PublicationNo. 2009/0234106, which is herein incorporated by reference in itsentirety, particularly in parts pertinent to proteins that bind ActivinA;

TGF-beta specific antibodies, peptibodies, related proteins, and thelike, including but not limited to those described in U.S. Pat. No.6,803,453 and U.S. Publication No. 2007/0110747, each of which is hereinincorporated by reference in its entirety, particularly in partspertinent to proteins that bind TGF-beta;

Amyloid-beta protein specific antibodies, peptibodies, related proteins,and the like, including but not limited to those described in PCTPublication No. WO 2006/081171, which is herein incorporated byreference in its entirety, particularly in parts pertinent to proteinsthat bind amyloid-beta proteins. One antibody contemplated is anantibody having a heavy chain variable region comprising SEQ ID NO:8 anda light chain variable region having SEQ ID NO:6 as disclosed in theforegoing publication;

c-Kit specific antibodies, peptibodies, related proteins, and the like,including but not limited to those described in U.S. Publication No.2007/0253951, which is incorporated herein by reference in its entirety,particularly in parts pertinent to proteins that bind c-Kit and/or otherstem cell factor receptors;

OX40L specific antibodies, peptibodies, related proteins, and the like,including but not limited to those described in U.S. Publication No.2006/0002929, which is incorporated herein by reference in its entirety,particularly in parts pertinent to proteins that bind OX40L and/or otherligands of the OX40 receptor; and

Other exemplary proteins, including Activase® (alteplase, tPA); Aranesp®(darbepoetin alfa); Epogen® (epoetin alfa, or erythropoietin); GLP-1,Avonex® (interferon beta-1a); Bexxar® (tositumomab, anti-CD22 monoclonalantibody); Betaseron® (interferon-beta); Campath® (alemtuzumab,anti-CD52 monoclonal antibody); Dynepo® (epoetin delta); Velcade®(bortezomib); MLN0002 (anti-α4β7 mAb); MLN1202 (anti-CCR2 chemokinereceptor mAb); Enbrel® (etanercept, TNF-receptor/Fc fusion protein, TNFblocker); Eprex® (epoetin alfa); Erbitux® (cetuximab,anti-EGFR/HER1/c-ErbB-1); Genotropin® (somatropin, Human GrowthHormone); Herceptin® (trastuzumab, anti-HER2/neu (erbB2) receptor mAb);Humatrope® (somatropin, Human Growth Hormone); Humira® (adalimumab);insulin in solution; Infergen® (interferon alfacon-1); Natrecor®(nesiritide; recombinant human B-type natriuretic peptide (hBNP);Kineret® (anakinra); Leukine® (sargamostim, rhuGM-CSF); LymphoCide®(epratuzumab, anti-CD22 mAb); Benlysta™ (lymphostat B, belimumab,anti-BlyS mAb); Metalyse® (tenecteplase, t-PA analog); Mircera® (methoxypolyethylene glycol-epoetin beta); Mylotarg® (gemtuzumab ozogamicin);Raptiva® (efalizumab); Cimzia® (certolizumab pegol, CDP 870); Soliris™(eculizumab); pexelizumab (anti-C5 complement); Numax® (MEDI-524);Lucentis® (ranibizumab); Panorex® (17-1A, edrecolomab); Trabio®(lerdelimumab); TheraCim hR3 (nimotuzumab); Omnitarg (pertuzumab, 2C4);Osidem® (IDM-1); OvaRex® (B43.13); Nuvion® (visilizumab); cantuzumabmertansine (huC242-DM1); NeoRecormon® (epoetin beta); Neumega®(oprelvekin, human interleukin-11); Neulasta® (pegylated filgastrim,pegylated G-CSF, pegylated hu-Met-G-CSF); Neupogen® (filgrastim, G-CSF,hu-MetG-CSF); Orthoclone OKT3® (muromonab-CD3, anti-CD3 monoclonalantibody); Procrit® (epoetin alfa); Remicade® (infliximab, anti-TNFαmonoclonal antibody); Reopro® (abciximab, anti-GP 1Ib/Ilia receptormonoclonal antibody); Actemra® (anti-IL6 Receptor mAb); Avastin®(bevacizumab), HuMax-CD4 (zanolimumab); Rituxan® (rituximab, anti-CD20mAb); Tarceva® (erlotinib); Roferon-A®-(interferon alfa-2a); Simulect®(basiliximab); Prexige® (lumiracoxib); Synagis® (palivizumab); 146B7-CHO(anti-IL15 antibody, see U.S. Pat. No. 7,153,507); Tysabri®(natalizumab, anti-α4integrin mAb); Valortim® (MDX-1303, anti-B.anthracia protective antigen mAb); ABthrax™; Vectibix® (panitumumab);Xolair® (omalizumab); ETI211 (anti-MRSA mAb); IL-1 trap (the Fc portionof human IgG1 and the extracellular domains of both IL-1 receptorcomponents (the Type I receptor and receptor accessory protein)); VEGFtrap (Ig domains of VEGFR1 fused to IgG1 Fc); Zenapax® (daclizumab);Zenapax® (daclizumab, anti-IL-2Ra mAb); Zevalin® (ibritumomab tiuxetan);Zetia® (ezetimibe); Orencia® (atacicept, TACI-Ig); anti-CD80 monoclonalantibody (galiximab); anti-CD23 mAb (lumiliximab); BR2-Fc (huBR3/huFcfusion protein, soluble BAFF antagonist); CNTO 148 (golimumab, anti-TNFαmAb); HGS-ETR1 (mapatumumab; human anti-TRAIL Receptor-1 mAb);HuMax-CD20 (ocrelizumab, anti-CD20 human mAb); HuMax-EGFR (zalutumumab);M200 (volociximab, anti-α5β1 integrin mAb); MDX-010 (ipilimumab,anti-CTLA-4 mAb and VEGFR-1 (IMC-18F1); anti-BR3 mAb; anti-C. difficileToxin A and Toxin B C mAbs MDX-066 (CDA-1) and MDX-1388); anti-CD22dsFv-PE38 conjugates (CAT-3888 and CAT-8015); anti-CD25 mAb (HuMax-TAC);anti-CD3 mAb (NI-0401); adecatumumab; anti-CD30 mAb (MDX-060); MDX-1333(anti-IFNAR); anti-CD38 mAb (HuMax CD38); anti-CD40L mAb; anti-CriptomAb; anti-CTGF Idiopathic Pulmonary Fibrosis Phase I Fibrogen (FG-3019);anti-CTLA4 mAb; anti-eotaxin1 mAb (CAT-213); anti-FGF8 mAb;anti-ganglioside GD2 mAb; anti-ganglioside GM2 mAb; anti-GDF-8 human mAb(MYO-029); anti-GM-CSF Receptor mAb (CAM-3001); anti-HepC mAb (HuMaxHepC); anti-IFNα mAb (MEDI-545, MDX-1103); anti-IGF1R mAb; anti-IGF-1RmAb (HuMax-Inflam); anti-IL12 mAb (ABT-874); anti-IL12/IL23 mAb (CNTO1275); anti-IL13 mAb (CAT-354); anti-IL2Ra mAb (HuMax-TAC); anti-IL5Receptor mAb; anti-integrin receptors mAb (MDX-018, CNTO 95); anti-IP10Ulcerative Colitis mAb (MDX-1100); anti-LLY antibody; BMS-66513;anti-Mannose Receptor/hCGβ mAb (MDX-1307); anti-mesothelin dsFv-PE38conjugate (CAT-5001); anti-PD1mAb (MDX-1106 (ONO-4538)); anti-PDGFRαantibody (IMC-3G3); anti-TGFβ mAb (GC-1008); anti-TRAIL Receptor-2 humanmAb (HGS-ETR2); anti-TWEAK mAb; anti-VEGFR/Flt-1 mAb; anti-ZP3 mAb(HuMax-ZP3); NVS Antibody #1; and NVS Antibody #2.

Also included can be a sclerostin antibody, such as but not limited toromosozumab, blosozumab, or BPS 804 (Novartis). Further included can betherapeutics such as rilotumumab, bixalomer, trebananib, ganitumab,conatumumab, motesanib diphosphate, brodalumab, vidupiprant,panitumumab, denosumab, NPLATE, PROLIA, VECTIBIX or XGEVA. Additionally,included in the device can be a monoclonal antibody (IgG) that bindshuman Proprotein Convertase Subtilisin/Kexin Type 9 (PCSK9). Such PCSK9specific antibodies include, but are not limited to, Repatha®(evolocumab) and Praluent® (alirocumab), as well as molecules, variants,analogs or derivatives thereof as disclosed in the following patents orpatent applications, each of which is herein incorporated by referencein its entirety for all purposes: U.S. Pat. No. 8,030,547, U.S.Publication No. 2013/0064825, WO2008/057457, WO2008/057458,WO2008/057459, WO2008/063382, WO2008/133647, WO2009/100297,WO2009/100318, WO2011/037791, WO2011/053759, WO2011/053783,WO2008/125623, WO2011/072263, WO2009/055783, WO2012/0544438,WO2010/029513, WO2011/111007, WO2010/077854, WO2012/088313,WO2012/101251, WO2012/101252, WO2012/101253, WO2012/109530, andWO2001/031007.

Also included can be talimogene laherparepvec or another oncolytic HSVfor the treatment of melanoma or other cancers. Examples of oncolyticHSV include, but are not limited to talimogene laherparepvec (U.S. Pat.Nos. 7,223,593 and 7,537,924); OncoVEXGALV/CD (U.S. Pat. No. 7,981,669);OrienX010 (Lei et al. (2013), World J. Gastroenterol., 19:5138-5143);G207, 1716; NV1020; NV12023; NV1034 and NV1042 (Vargehes et al. (2002),Cancer Gene Ther., 9(12):967-978).

Also included are TIMPs. TIMPs are endogenous tissue inhibitors ofmetalloproteinases (TIMPs) and are important in many natural processes.TIMP-3 is expressed by various cells or and is present in theextracellular matrix; it inhibits all the major cartilage-degradingmetalloproteases, and may play a role in role in many degradativediseases of connective tissue, including rheumatoid arthritis andosteoarthritis, as well as in cancer and cardiovascular conditions. Theamino acid sequence of TIMP-3, and the nucleic acid sequence of a DNAthat encodes TIMP-3, are disclosed in U.S. Pat. No. 6,562,596, issuedMay 13, 2003, the disclosure of which is incorporated by referenceherein. Description of TIMP mutations can be found in U.S. PublicationNo. 2014/0274874 and PCT Publication No. WO 2014/152012.

Also included are antagonistic antibodies for human calcitoningene-related peptide (CGRP) receptor and bispecific antibody moleculethat target the CGRP receptor and other headache targets. Furtherinformation concerning these molecules can be found in PCT ApplicationNo. WO 2010/075238.

Additionally, bispecific T cell engager (BiTE®) antibodies, e.g.BLINCYTO® (blinatumomab), can be used in the device. Alternatively,included can be an APJ large molecule agonist e.g., apelin or analoguesthereof in the device. Information relating to such molecules can befound in PCT Publication No. WO 2014/099984.

In certain embodiments, the medicament comprises a therapeuticallyeffective amount of an anti-thymic stromal lymphopoietin (TSLP) or TSLPreceptor antibody. Examples of anti-TSLP antibodies that may be used insuch embodiments include, but are not limited to, those described inU.S. Pat. Nos. 7,982,016, and 8,232,372, and U.S. Publication No.2009/0186022. Examples of anti-TSLP receptor antibodies include, but arenot limited to, those described in U.S. Pat. No. 8,101,182. Inparticularly preferred embodiments, the medicament comprises atherapeutically effective amount of the anti-TSLP antibody designated asA5 within U.S. Pat. No. 7,982,016.

Although the computing system for modeling and parameter selection, druginjection device, methods, and elements thereof, have been described interms of exemplary embodiments, they are not limited thereto. Thedetailed description is to be construed as exemplary only and does notdescribe every possible embodiment of the invention because describingevery possible embodiment would be impractical, if not impossible.Numerous alternative embodiments could be implemented, using eithercurrent technology or technology developed after the filing date of thispatent that would still fall within the scope of the claims defining theinvention.

It should be understood that the legal scope of the invention is definedby the words of the claims set forth at the end of this patent. Theappended claims should be construed broadly to include other variantsand embodiments of same, which may be made by those skilled in the artwithout departing from the scope and range of equivalents of thecomputing systems, drug delivery devices, systems, methods, and theirelements.

1. A non-transitory computer-readable medium storing thereoninstructions that, when executed on one or more processors, implement amethod for determining predicted failure rates of drug injectiondevices, the method comprising: receiving a set of parameters thatspecify physical properties of (i) a syringe, and (ii) a liquid drug,and (iii) a drug injection device configured to deliver the liquid drugto a patient via the syringe; receiving failure rate data that specifiesa measured rate of failure of the drug injection device in response tovarious peak pressures within the syringe; applying the received set ofparameters to a kinematic model of the drug injection device todetermine a predicted peak pressure within the syringe, includingdetermining the predicted peak pressure as a function of impact velocityof the liquid drug; determining a probability of failure of the druginjection device using (i) the received failure rate data and (ii) thepredicted peak pressure; and providing an indication of the determinedprobability of failure to an output device.
 2. The computer-readablemedium of claim 1, wherein the implemented method further comprisesmodeling a fluid column in the syringe as an acoustic medium.
 3. Thecomputer-readable medium of claim 1, wherein the implemented methodfurther comprises modeling a fluid column in the syringe using aKorteweg equation.
 4. The computer-readable medium of claim 1, whereinthe drug injection device includes a mechanism configured to drive aplunger rod toward a plunger of the syringe encased in a syringecarrier, wherein the plunger rod advances the syringe carrier toward afront shell of the drug delivery device; the implemented method furthercomprising: using a one-dimensional (1D) kinematic model to modelinteractions between at least the mechanism, the plunger rod, theplunger, the syringe carrier.
 5. The computer-readable medium of claim4, wherein using the 1D kinematic model includes (A) modeling themechanism as a linear spring with an equilibrium length, and/or (B)modeling (i) a pre-impact stage at which the plunger rod has not come incontact with the plunger, (ii) a first impact stage at which the plungerrod comes in contact with the plunger, and (iii) a third impact stage atwhich the syringe carrier comes in contact with the front shell. 6.(canceled)
 7. The computer-readable medium of claim 1, wherein receivingthe set of parameters to the kinematic model includes receivinggeometric parameters related to at least one of the syringe or the druginjection device, including at least one of: (i) plunger depth, (ii)plunger rod wall thickness, (iii) plunger rod activation length, (iv)syringe barrel diameter, (v) syringe wall thickness, (vi) fluid volume,(vii) syringe carrier activation length, (viii) plunger rod depth, (ix)length of the guide rod, (x) length of guide rod base, (xi) length ofneedle insertion, (xii) needle length, (xiii) needle, or (xiv) un-sprunglength of spring.
 8. (canceled)
 9. The computer-readable medium of claim1, wherein receiving the set of parameters to the kinematic modelincludes receiving parameters indicative of masses of components,including at least one of: (i) mass of syringe carrier, (ii) mass ofpre-filled syringe with drug, (iii) mass of plunger, (iv) mass of rod,or (iv) mass of spring.
 10. (canceled)
 11. The computer-readable mediumof claim 1, wherein receiving the set of parameters to the kinematicmodel includes receiving at least one of the following (a) through (f):(a) a parameter indicative of plunger elasticity, (b) a parameterindicative of front shell elasticity, (c) a parameter indicative offluid sound speed, (d) a parameter indicative of viscosity of the drug,(e) a spring constant, and/or (f) experimental data indicative of aplurality of test runs of an actual drug injector device that shares atseveral physical properties with the drug injection device beingmodeled, and deriving one or more of (i) syringe driver friction, (ii)internal plunger damping, (iii) plunger-syringe friction, and (iv) ashell damping constant from the experimental data. 12-16. (canceled) 17.The computer-readable medium of claim 1, wherein determining theprobability of failure of the drug injection device includes applying atwo-term Weibull distribution function.
 18. A method for manufacturingdrug injection devices, the method comprising: receiving, by one or moreprocessors, a fixed set of parameters that specify physical propertiesof a syringe and a liquid drug; determining a set of parameters thatspecify physical properties of a drug injection device configured todeliver the liquid drug to a patient via the syringe, including: (i)generating, by the one or more processors, a candidate set of parametersfor the drug injection device; (ii) applying, by the one or moreprocessors, the fixed set of parameters and the candidate set ofparameters to a kinematic model of the drug injection device todetermine a predicted peak pressure within the syringe, includingdetermining the predicted peak pressure as a function of impact velocityof the liquid drug, (iii) determining, by the one or more processors, aprobability of failure of the drug injection device using the determinedpredicted peak pressure, (iv) if the probability of failure is above athreshold value, repeating the steps (i)-(iii) with a modified candidateset of parameters, and (v) selecting the candidate set of parameters ifthe probability of failure is not above the threshold value; andmanufacturing the drug injection device using the determined set ofparameters.
 19. The method of claim 18, further comprising modeling afluid column in the syringe as an acoustic media.
 20. The method ofclaim 18, further comprises modeling a fluid column in the syringe usinga Korteweg equation.
 21. The method of claim 18, wherein the druginjection device includes a mechanism configured to drive a plunger rodtoward a plunger of the syringe encased in a syringe carrier, whereinthe plunger rod advances the syringe carrier toward a front shell of thedrug delivery device; the method further comprising: using aone-dimensional (1D) kinematic model to model interactions between atleast the mechanism, the plunger rod, the plunger, the syringe carrier.22. The method of claim 21, wherein using the 1D kinematic modelincludes (A) modeling the mechanism as a linear spring with anequilibrium length, and/or (B) modeling (i) a pre-impact stage at whichthe plunger rod has not come in contact with the plunger, (ii) a firstimpact stage at which the plunger rod comes in contact with the plunger,and (iii) a third impact stage at which the syringe carrier comes incontact with the front shell.
 23. (canceled)
 24. The method of claim 18,wherein receiving the set of parameters that specify the physicalproperties of the drug injection device includes receiving at least oneof the following (a) through (h): (a) geometric parameters for one orseveral components of the drug injection device, (b) parametersindicative of masses of components of the drug injection device (c) aparameter indicative of front shell elasticity, (d) a parameterindicative of plunger elasticity, (e) a parameter indicative of fluidsound speed, (f) a parameter indicative of viscosity of the drug, (g) aspring constant, and/or (h) experimental data indicative of a pluralityof test runs of an actual drug injector device that shares at severalphysical properties with the drug injection device being modeled, andderiving one or more of (i) syringe driver friction, (ii) internalplunger damping, (iii) plunger-syringe friction, and (iv) a shelldamping constant from the experimental data. 25-31. (canceled)
 32. Adrug injection device configured to deliver a liquid drug to a patientvia a syringe, the drug injection device prepared by a processcomprising: receiving a fixed set of parameters that specify physicalproperties of a syringe and a liquid drug; determining a set ofparameters that specify physical properties of a drug injection deviceconfigured to deliver the liquid drug to a patient via the syringe,including: (i) generating a candidate set of parameters for the druginjection device; (ii) applying the fixed set of parameters and thecandidate set of parameters to a kinematic model of the drug injectiondevice to determine a predicted peak pressure within the syringe,including determining the predicted peak pressure as a function ofimpact velocity of the liquid drug, (iii) determining a probability offailure of the drug injection device using the determined predicted peakpressure, (iv) if the probability of failure is above a threshold value,repeating the steps (i)-(iii) with a modified candidate set ofparameters, and (v) selecting the candidate set of parameters if theprobability of failure is not above the threshold value; and using thedetermined set of parameters to manufacture the drug injection device.33. The drug injection device of claim 32, wherein the process furthercomprises modeling a fluid column in the syringe as an acoustic media.34. The drug injection device of claim 32, wherein the process furthercomprises modeling a fluid column in the syringe using a Kortewegequation.
 35. The drug injection device of claim 32, comprising: aplunger rod; a syringe carrier in which the syringe is encased; a frontshell; a mechanism configured to drive the plunger rod toward a plungerof the syringe, wherein the plunger rod advances the syringe carriertoward the front shell; wherein the process further comprises using aone-dimensional (1 D) kinematic model to model interactions between atleast the mechanism, the plunger rod, the plunger, the syringe carrier.